Stardust in the TEM

Fraundorf, P.; Fraundorf, G. K.; Bernatowicz, T. J.; Lewis, R. S.; Tang, Ming

doi:10.1016/0304-3991(89)90008-9

Cited by 45 publications

(19 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now integrative views of lattice information in digital images yield new challenges for mathematical harmonic analysis [3]. Such challenges are illustrated by a series of notes [4][5][6][7] on the uses and shortcomings of "weakly convergent" Fourier transform window techniques. Here, we show how robust (if pedestrian) digital darkfield techniques help to characterize: (i) an Antimony-doped Tin Oxide nanoparticle screw dislocation, and (ii) twinning and strain in a gold decahedral twin.…”

mentioning

confidence: 99%

Digital Darkfield Analysis of Nanoparticle Defects

Fraundorf

Liu

Mandell

2007

MAM

View full text Add to dashboard Cite

Microscopists have done combined space and frequency decompositions optically since long before coining of the word "wavelet" [1], under the name "darkfield imaging" [2]. Now integrative views of lattice information in digital images yield new challenges for mathematical harmonic analysis [3]. Such challenges are illustrated by a series of notes [4][5][6][7] on the uses and shortcomings of "weakly convergent" Fourier transform window techniques. Here, we show how robust (if pedestrian) digital darkfield techniques help to characterize: (i) an Antimony-doped Tin Oxide nanoparticle screw dislocation, and (ii) twinning and strain in a gold decahedral twin.Each row in the figures at right contains a power spectrum used to select a reference "g-vector" of interest, followed by a complex-color map of darkfield amplitude (intensity) and phase (hue) with respect to that g-vector. The remaining two columns use coordinate-color to show isotropic strain (red is compressed, cyan is expanded) and shear strain (chartreuse is clockwise and indigo is counter clockwise) with respect to that reference. Each pixel in these is a fractional strain measurement.The (110) planes in the ATO grain of Fig. 1 (top row) show a 180 degree phase-lag between the top and bottom half of the crystal in the darkfield, in spite of the spacing uniformity (seen in both the phase beats of the complex darkfield image, and comparable top/bottom intensities in the strain maps). The other reflections (e.g. rows 2 and 3) do not share this phase lag, indicating that the (110) planes indeed form a "spiral staircase" running from left to right that moves up by ½ g 110 = 0.167nm for each half-turn. Quantitative information on the rate of strain relaxation around this dislocation [cf. 8] is available in this image as well.Digital darkfield analysis of the gold decahedral grain near the 5-fold zone in Fig. 2 shows singleslice wedges for (200) and (220) reflections, in place of the "bowties" seen for icosahedral twins [7], and double-slice wedges for (111) reflections in place of icotwin "butterflies". Notice also the absence of a (111) discontinuity bisecting the double-slice wedges. This puts picometer-scale limits on the bulk-driven build up of strain between sub-domains in this tiny particle.

show abstract

mentioning

confidence: 99%

Digital Darkfield Analysis of Nanoparticle Defects

Fraundorf

Liu

Mandell

2007

MAM

View full text Add to dashboard Cite

show abstract

“…

…”

mentioning

confidence: 99%

Digital Darkfield Tableaus

et al. 2006

View full text Add to dashboard Cite

Like wavelet decompositions, power spectra "tiled with direct space maps" are versions of a lattice image intermediate between direct and reciprocal space [1]. They generally take about the same time to calculate as a power spectrum, and contain useful information of all sorts about "where periodicities lie". Questions of this sort will be of increasing importance e.g. in subångstrom resolution pictures. The information is useful in spite of the fact that members of the mathematical harmonic analysis community have long moved past the sharp edged Fourier apertures that electron optical darkfield requires [2]. By illustrating useful applications for sharp-edged tilings, we might thus inspire the math community to look at the much wider range of pattern recognition problems that today's high resolution electron microscopists face.The first tiling we discuss is the one most familiar to microscopists: Amplitude tableaus. It's familiar because the inverse transform (bandpass image) of an apertured Fourier transform (or diffraction pattern) has phase and amplitude components, but only the latter are detectable in optical darkfield images recorded on film. They are also optically tedious to set up. Digitally on the other hand, a 1024x1024 image yields a tableau of 32x32 complex bandpass images in only seconds on a modern computer, the amplitude version of which corresponds (in terms of bandpass) to 1023 darkfield and one brightfield image taken with the microscope. Because individual tiles with spatial correlations easily catch one's eye, one can quickly examine the tableau for regions of hidden periodicity, as well as for regions of characteristic shape (like the bowties and butterflies characteristic of icosahedral twins in the example of Fig. 1).The other tilings we mention here are Isotropic and Shear Strain tableaus. These exploit the idea that phase in the bandpass image measures displacement, so that phase gradient measures periodicity deviations from the bandpass reference [3]. This technique has been applied, one periodicity at a time, for example to measure interface and dislocation strain [4,5]. Fig. 2 illustrates how a tableau of isotropic (parallel to the reference g-vector) and shear (perpendicular to the g-vector) strain tiles in effect yield "diffraction contrast images" from a whole range of operating reflections. Here we use opposing hues red and cyan to represent relative compression and expansion, respectively, in the isotropic maps, and the orthogonal hues indigo and chartreuse to represent CCW and CW rotation, respectively, in the shear maps.

show abstract

“…relaxation processes can be studied. Mathematical transforms intermediate between direct and reciprocal space make possible digital darkfield strategies for mapping strain relaxation around interfaces and dislocations [1][2][3][4][5]. Here we examine applications to the measurement of lattice parameter differences between adjacent phases.…”

mentioning

confidence: 99%

Picometer Scale Differences of Lattice Spacing In TEM Images

Rose

Fraundorf

2006

Microsc Microanal

View full text Add to dashboard Cite

There are many applications in modern science in which a very precise knowledge of atom spacings i.e. lattice parameters is crucial. These include multi layer hetero structures in device manufacturing and core-rim nano particles, for example. In general it is interesting to know the change in spacings -or the strain -in the proximity of a lattice defect or a coherent interface between two different substances. From the knowledge of the spacings e.g. relaxation processes can be studied. Mathematical transforms intermediate between direct and reciprocal space make possible digital darkfield strategies for mapping strain relaxation around interfaces and dislocations [1][2][3][4][5]. Here we examine applications to the measurement of lattice parameter differences between adjacent phases.A digitized photograph of a HRTEM image serves as input. The FFT is calculated to obtain the power spectrum (PS). One spot in the PS is chosen as a reference frequency, although the precise reference frequency (g-vector) will be chosen later. Next a smooth aperture centered around the chosen point is applied, and the data is shifted so that the reference point is at the DC peak. Calculating the inverse FFT of the shifted data yields a complex image, which can be interpreted as a darkfield (DF) image. Measurements can only be made at relatively bright areas in the DF image. The phase-gradient of the complex data parallel to the g-vector can be interpreted as a strain map. The actual value at each point in the strain map -referred to as d -describes the deviation of the frequency (i.e. spacing) at this point in the image from the chosen reference frequency. Our algorithm minimizes d by varying the g-vector, as the measurements on computer generated images were most precise when d is minimal. The result of the measurement algorithm is the spacing that corresponds to the chosen base frequency multiplied by 1+d. It's a strength of this method that the result does not depend on the reference (i.e. g-vector) chosen by the user. Fig. 1 shows the computer generated input where atoms are represented by Gaussian shaped peaks at positions marked by a 2D Bravais lattice [4]. As the arrangement of atoms is periodic straight lines can be drawn and parallels can be found. The distance between these parallels defines the spacing. The solid line in Fig. 1 marks the point, where the length of one base vector is multiplied by 1.012 which leads to a step in various spacings. At another position the base vector is multiplied again by 1.006. The upper right shows the PS and the g-vector of the spacing that was examined. At the upper left corner of the input the spacing is 5.3853 pixels. Fig. 2 shows the strain map which clearly shows the two steps in spacing, the three regions with constant spacing that appear flat in the strain map and the spacings determined by the algorithm. The error in the spacings measured is less than 1%! Fig. 3 shows one of the two different regions of the same HRTEM image where measurements were made to show that variations in the...

show abstract

Stardust in the TEM

Cited by 45 publications

References 12 publications

Digital Darkfield Analysis of Nanoparticle Defects

Digital Darkfield Analysis of Nanoparticle Defects

Digital Darkfield Tableaus

Picometer Scale Differences of Lattice Spacing In TEM Images

Contact Info

Product

Resources

About